Question

The difference between the ages of two sisters is$10$ years. If $15$ years ago, the elder one was twice $10$ years. If $15$ years ago, the elder one was twice as old as the younger one, find their present ages.

Answer 1

Let age of two sisters be x and y,

$x-y=10$ (1)

$x-15=20$ (2)

$x-15=2(y-15)$ (3)

Substituting (2) in (3)

$20=2y-30$

$50=2y$

$y=25$ (4)

Substituting (4) in (1)

$x-25=10$

$x=35$

Their present ages are 35 years and 25 years.